# Minimal immersed manifold

From Diffgeom

*This article defines a property that makes sense for a Riemannian metric over a differential manifold*

*This is the property of the following curvature being everywhere zero*: Mean curvature

## Definition

### Symbol-free definition

A Riemannian manifold (viz a differential manifold equipped with a Riemannian metric) is termed a **minimal manifold** if the mean curvature of the manifold is zero at all points. This is a generalization to the manifold setting of the notion of a minimal surface.